Abstract
Equations related to the sums of the products of multivariate polynomials are studied. One set of polynomials is considered as determined and the other is sought. In the general case of defining polynomials, a series of relationships is obtained for the degrees of polynomials and determinants of matrices composed of polynomial coefficients. On the basis of these relationships and the continuity equation, a number of variants of covariant vectors of limited current density are presented. The results can definitely be considered correct if the accelerations are not too large. The case where the current vector depends on the variable whose value at transition to the stationary state is dictated by the conditions under which such a transition is treated (if these conditions are unknown, then particular elements of uncertainty are possible in the stationary states).
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ACKNOWLEDGMENTS
The author thanks A.V. Borisov for his scientific advice and aid in the work.
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Translated by E. Oborin
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Ependiev, M.B. On Multivariate Polynomials and Construction of Covariant Bounded Current Vectors. Moscow Univ. Phys. 75, 309–315 (2020). https://doi.org/10.3103/S0027134920040074
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DOI: https://doi.org/10.3103/S0027134920040074